How to model an accurate parabolic mirror with a known focal point?
Add mesh z surface

Enable the add mesh extra objects addon, then from add menu choose add &gt; mesh &gt; math function &gt; math z surface

The equation of a paraboloid with focus f is 

(x ** 2 + y ** 2) / (4 * f)



paraboloid with focus at (0, 0, 1)


Thickness can be added with the solidify modifier.